reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem Th21: ::EUCLID_2:20
  for x1,x2 being Element of REAL n,a being Real holds |(a*
  x1,x2)| = a*|(x1,x2)|
proof
  let x1,x2 be Element of REAL n,a be Real;
  len x1 = n & len x2 = n by CARD_1:def 7;
  hence thesis by RVSUM_1:121;
end;
